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The Geometry of Physics by Theodore Frankel

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CHAPTER 8

The Geometry of Surfaces in. image3

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The geometry or kinematics of this subject is a great contrast to that of the flexible line, and, in its merest elements, presents ideas not very easily apprehended, and subjects of investigation that have exercised, and perhaps overtasked, the powers of some of the greatest mathematicians.

Kelvin and Tait, Elements of Natural Philosophy

8.1. The First and Second Fundamental Forms

What is the length of a curve that leaves the north pole, ends at the south pole, and makes a constant angle with each meridian ...

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